{
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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  },
  "orig_nbformat": 2,
  "kernelspec": {
   "name": "python_defaultSpec_1600326590699",
   "display_name": "Python 3.7.4 64-bit ('base': conda)"
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 "nbformat": 4,
 "nbformat_minor": 2,
 "cells": [
  {
   "source": [
    "# 使用梯度上升法求解主成分"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.empty((100, 2))\n",
    "X[:,0] = np.random.uniform(0., 100., size=100)\n",
    "X[:,1] = 0.75 * X[:,0] + 3. + np.random.normal(0, 10., size=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## demean"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def demean(X):\n",
    "    return X - np.mean(X, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_demean = demean(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(X_demean[:,0], X_demean[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.9184653865522706e-15"
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "source": [
    "np.mean(X_demean[:,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "1.48858703141741e-14"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "np.mean(X_demean[:,1])\n"
   ]
  },
  {
   "source": [
    "## 梯度上升法"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(w, X):\n",
    "    return np.sum((X.dot(w)**2)) / len(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def df_math(w, X):\n",
    "    return X.T.dot(X.dot(w))* 2. / len(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def df_debug(w, X, epsilon=0.0001):\n",
    "    res = np.empty(len(w))\n",
    "    for i in range(len(w)):\n",
    "        w_1 = w.copy()\n",
    "        w_1[i] += epsilon\n",
    "        w_2 = w.copy()\n",
    "        w_2[i] -= epsilon\n",
    "        res[i] = (f(w_1, X) - f(w_2, X)) / (2 * epsilon)\n",
    "    return res"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def direction(w):\n",
    "    return w / np.linalg.norm(w)\n",
    "\n",
    "def gradient_ascent(df, X, initial_w, eta, n_iters=1e4, epsilon=1e-8):\n",
    "\n",
    "    w = direction(initial_w)\n",
    "    cur_iter = 0\n",
    "\n",
    "    while cur_iter < n_iters:\n",
    "        gradient = df(w, X)\n",
    "        last_w = w\n",
    "        w = w + eta * gradient\n",
    "        w = direction(w) # 每次求一个单位方向\n",
    "        if (abs(f(w, X) - f(last_w, X)) < epsilon):\n",
    "            break\n",
    "\n",
    "        cur_iter += 1\n",
    "    return w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0.59334043, 0.68484665])"
     },
     "metadata": {},
     "execution_count": 27
    }
   ],
   "source": [
    "initial_w = np.random.random(X.shape[1]) # 不能用0向量开始\n",
    "initial_w"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "eta = 0.001"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 不能使用standardscaler标准化数据"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0.77625564, 0.63041826])"
     },
     "metadata": {},
     "execution_count": 30
    }
   ],
   "source": [
    "gradient_ascent(df_debug, X_demean, initial_w, eta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([0.77625564, 0.63041826])"
     },
     "metadata": {},
     "execution_count": 31
    }
   ],
   "source": [
    "gradient_ascent(df_math, X_demean, initial_w, eta)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "text/plain": "<Figure size 432x288 with 1 Axes>",
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "w = gradient_ascent(df_math, X_demean, initial_w, eta)\n",
    "\n",
    "plt.scatter(X_demean[:,0], X_demean[:,1])\n",
    "plt.plot([0, w[0]*30], [0,w[1]*30], color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "X2 = np.empty((100, 2))\n",
    "X2[:,0] = np.random.uniform(0., 100., size=100)\n",
    "X2[:,1] = 0.75 * X2[:,0] + 3. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(X2[:,0], X2[:,1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "X2_demean = demean(X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "w2 = gradient_ascent(df_math, X2_demean, initial_w, eta)\n",
    "\n",
    "plt.scatter(X2_demean[:,0], X2_demean[:,1])\n",
    "plt.plot([0, w2[0]*30], [0,w2[1]*30], color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}